Product-Space.md

Linear SpacesProduct SpaceDefinition: Let (V,F)(V,F)(V,F) and (W,F)(W,F)(W,F) be two vector spaces over the same field FFF. The set V×WV \times WV×W is called the product space of VVV and WWW and is denoted by V×WV \times WV×W.
V×W={(v,w):v∈V,w∈W}V \times W = \{(v,w):v \in V, w \in W \}V×W={(v,w):v∈V,w∈W}
(v1,w1)+(v2,w2)=(v1+v2,w1+w2)(v_1,w_1) + (v_2,w_2) = (v_1 + v_2, w_1 + w_2)(v1​,w1​)+(v2​,w2​)=(v1​+v2​,w1​+w2​) (vector addition)
α(v,w)=(αv,αw)\alpha(v,w) = (\alpha v, \alpha w)α(v,w)=(αv,αw) (scalar multiplication)
#EE501 - Linear Systems Theory at METU